Your mileage may vary, but this is what it shows on my NAT router at
home. I'll only explain part of the output as not everything is directly
relevant.

We first see the loopback interface. While your computer may function
somewhat without one, I'd advise against it. The MTU size (Maximum Transfer
Unit) is 3924 octets, and it is not supposed to queue. Which makes sense
because the loopback interface is a figment of your kernel's imagination.

I'll skip the dummy interface for now, and it may not be present on your
computer. Then there are my two physical network interfaces, one at the side
of my cable modem, the other one serves my home ethernet segment.
Furthermore, we see a ppp0 interface.

Note the absence of IP addresses. iproute disconnects the concept of 'links'
and 'IP addresses'. With IP aliasing, the concept of 'the' IP address had
become quite irrelevant anyhow.

It does show us the MAC addresses though, the hardware identifier of our
ethernet interfaces.

This contains more information. It shows all our addresses, and to which
cards they belong. 'inet' stands for Internet (IPv4). There are lots of other
address families, but these don't concern us right now.

Let's examine eth0 somewhat closer. It says that it is related to the inet
address '10.0.0.1/8'. What does this mean? The /8 stands for the number of
bits that are in the Network Address. There are 32 bits, so we have 24 bits
left that are part of our network. The first 8 bits of 10.0.0.1 correspond
to 10.0.0.0, our Network Address, and our netmask is 255.0.0.0.

The other bits are connected to this interface, so 10.250.3.13 is directly
available on eth0, as is 10.0.0.1 for example.

With ppp0, the same concept goes, though the numbers are different. Its
address is 212.64.94.251, without a subnet mask. This means that we have a
point-to-point connection and that every address, with the exception of
212.64.94.251, is remote. There is more information, however. It tells us
that on the other side of the link there is, yet again, only one address,
212.64.94.1. The /32 tells us that there are no 'network bits'.

It is absolutely vital that you grasp these concepts. Refer to the
documentation mentioned at the beginning of this HOWTO if you have trouble.

You may also note 'qdisc', which stands for Queueing Discipline. This will
become vital later on.

Well, we now know how to find 10.x.y.z addresses, and we are able to reach
212.64.94.1. This is not enough however, so we need instructions on how to
reach the world. The Internet is available via our ppp connection, and it
appears that 212.64.94.1 is willing to spread our packets around the
world, and deliver results back to us.

This is pretty much self explanatory. The first 3 lines of output explicitly
state what was already implied by ip address show, the last line
tells us that the rest of the world can be found via 212.64.94.1, our
default gateway. We can see that it is a gateway because of the word
via, which tells us that we need to send packets to 212.64.94.1, and that it
will take care of things.